Operation of a gas turbine with gaseous fuel requires at least a combustible gas prepressure which must be at least as high as the pressure in the combustion chamber plus the pressure difference over the fuel system. The pressure difference is dependent largely on the volumetric fuel flow, i.e. under otherwise constant conditions on the mass fuel flow. Combustion chambers with premixing burners of the designs which have become known among others from EP 321 809, EP 780 629, WO 01/96785, WO 92/19913, WO 93/17279 require a comparatively high combustible gas pressure difference so that the combustible gas for premixed combustion can emerge with high momentum and finely distributed through the comparatively small fuel exit openings. In a modern gas turbine set which works for example in a high pressure combustion chamber with a combustible gas chamber pressure of 30 bar, for full load operation fuel pressures in the range from 40 to 50 or even 60 bar and more are required. The required combustible gas prepressure is conventionally specified in the design phase and must either be guaranteed by the gas distribution network, or expensive and complex gas compressor stations are necessary, operation of which furthermore consumes power produced by the gas turbine set, for example a power in the range from 2 to 5 MW. When the necessary combustible gas prepressure cannot be made available, the gas turbine set according to the prior art can only be operated with reduced power. Therefore the gas compressor stations are often made even redundantly; this means high additional capital expenditure.